Transport number by moving boundary

To calculate the transport numbers of sodium chloride from moving boundary measurements. 

The following data (Longsworth, J. Amer. Chem. Soc. 1932, 54, 2745) refer to the movement of a rising boundary between solutions of sodium and cadmium chlorides the lower electrode was a cadmium anode and the upper a silver/silver chloride cathode. The temperature was 25 C, the current was maintained constant at 16.00 x 10 int. A, the cross-sectional area of the tube was 0.1115 cm and the concentration of the sodium chloride 0.02 molel-. Table 1 gives some corresponding readings of the time t and the distance of traverse of the boundary x. 

If the concentration of sodium chloride is c and the boundary sweeps through a volume in a time t when I is the current flowing, then the fraction of the current in the sodium chloride solution carried by sodium ions is given by vcFJIt. This is the transport number and t- = 1—f -. 

From the given values of x and t we see that tjx lies between 344 and 346. To obtain an average value we take the slope of the straight line 

Longsworth (loc. cit.) applied a small correction for a displacement of the boundary due to volume changes behind the boundary at the anode, and for the conductance of the solvent. The magnitude of the correction in this case is only 0.0004, which is scarcely significant. 

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